Georgios Papafotiou

Model Predictive Direct Torque Control—Part I: Concept, Algorithm, and Analysis

This paper focuses on direct torque control (DTC) for three-phase AC electric drives. A novel model predictive control scheme is proposed that keeps the motor torque, the stator flux, and (if present) the inverters neutral point potential within given hysteresis bounds while minimizing the switching frequency of the inverter. Based on an internal model of the drive, the controller predicts several future switch transitions, extrapolates the output trajectories, and chooses the sequence of inverter switch positions (voltage vectors) that minimizes the switching frequency. The advantages of the proposed controller are twofold. First, as underlined by the experimental results in the second part of this paper, it yields a superior performance with respect to the industrial state of the art. Specifically, the switching frequency is reduced by up to 50% while the torque and flux are kept more accurately within their bounds. Moreover, the fast dynamic torque response is inherited from standard DTC. Second, the scheme is applicable to a large class of (three-phase) AC electric machines driven by inverters.

Model Predictive Direct Torque Control—Part II: Implementation and Experimental Evaluation

This paper describes the implementation of the model predictive direct torque control (MPDTC) algorithm for the control of three-phase induction motor drives comprising a three-level DC-link inverter. The MPDTC scheme is designed to keep the motor torque and stator flux and the inverters neutral point potential within given hysteresis bounds while reducing the average switching frequency of the inverter, in comparison with the standard direct torque control (DTC) method. The algorithm is embedded in the control software environment of ABBs ACS6000 medium-voltage drive, and experimental results are provided which verify the advantageous features of MPDTC in terms of average inverter switching frequency reduction. More specifically, compared to standard DTC, the proposed MPDTC scheme achieves an average (over the whole operating range) reduction of the inverter switching frequency of 16.5%, but for specific operating conditions the reduction is as much as 37.4%.

Comparison of Hybrid Control Techniques for Buck and Boost DC-DC Converters

Five recent techniques from hybrid and optimal control are evaluated on two power electronics benchmark problems. The benchmarks involve a number of practically interesting operating scenarios for fixed-frequency synchronous dc-dc converters. The specifications are defined such that good performance can only be obtained if the switched and nonlinear nature of the problem is accounted for during the design phase. A nonlinear action is featured in all methods either intrinsically or as external logic. The designs are evaluated and compared on the same experimental platform. Experiments show that the proposed methods display high performances, while respecting circuit constraints, thus protecting the semiconductor devices. Moreover, the complexity of the controllers is compatible with the high-frequency requirements of the considered application.

Hybrid Model Predictive Control of the Step-Down DC–DC Converter

DC-DC converters pose challenging hybrid control problems, since the semiconductor switches induce different modes of operation and several constraints (on the duty cycle and the inductor current) are present. In this paper, we propose a novel approach to the modeling and controller design problem for fixed-frequency DC-DC converters, using a synchronous step-down DC-DC converter as an illustrative example. We introduce a hybrid converter model that is valid for the whole operating regime. Based on this model, we formulate and solve a constrained optimal control problem. To make the scheme implementable, we derive offline the explicit state-feedback control law, which can be easily stored and implemented in a lookup table. A Kalman filter is added to account for unmeasured load variations and to achieve zero steady-state output voltage error. An a posteriori analysis proves, by deriving a piecewise-quadratic Lyapunov function, that the closed-loop system is exponentially stable. Simulation results demonstrate the potential advantages of the proposed control methodology.

Model Predictive Control in Power Electronics: A Hybrid Systems Approach

The field of power electronics poses challenging control problems that cannot be treated in a complete manner using traditional modelling and controller design approaches. The main difficulty arises from the hybrid nature of these systems due to the presence of semiconductor switches that induce different modes of operation and operate with a high switching frequency. Since the control techniques traditionally employed in industry feature a significant potential for improving the performance and the controller design, the field of power electronics invites the application of advanced hybrid systems methodologies. The computational power available today and the recent theoretical advances in the control of hybrid systems allow one to tackle these problems in a novel way that improves the performance of the system, and is systematic and implementable. In this paper, this is illustrated by two examples, namely the Direct Torque Control of three-phase induction motors and the optimal control of switch-mode dc-dc converters.

Model Predictive Pulse Pattern Control

Industrial applications of medium-voltage drives impose increasingly stringent performance requirements, particularly with regards to harmonic distortions of the phase currents of the controlled electrical machine. An established method to achieve very low current distortions during steady-state operation is to employ offline calculated optimized pulse patterns (OPP). Achieving high dynamic performance, however, proves to be very difficult in a system operated by OPPs. In this paper, we propose a method that combines the optimal steady-state performance of OPPs with the very fast dynamics of trajectory tracking control. A constrained optimal control problem with a receding horizon policy, i.e. model predictive control (MPC), is formulated and solved. Results show that the combination of MPC with OPPs satisfies both the strict steady-state as well as the dynamic performance requirements imposed by the most demanding industrial applications. This is achieved without resorting to complicated structures such as observers of the state variable fundamental components of the electrical machine, which are required by state-of-the-art methods. A further advantage of the MPC method is the use of a receding horizon policy to provide feedback and a high degree of robustness.

Constrained Optimal Control of the Step-Down DC–DC Converter

In this paper, we propose a novel approach to the modeling and controller design of the synchronous step-down dc-dc converter. We introduce a hybrid converter model that is valid for the whole operating regime and captures the different modes of operation. Based on this model, we formulate and solve a constrained optimal control problem. This allows a systematic controller design that achieves the regulation of the output voltage to its reference despite input voltage and output load variations while satisfying the constraints on the duty cycle and the inductor current. The resulting state-feedback control law is of piecewise affine form, which can be easily stored and implemented in a lookup table. A Kalman filter is added to account for unmeasured load variations and to achieve zero steady-state output voltage error. Experimental results demonstrate the potential advantages of the proposed control methodology.

On the Optimal Control of Switch-Mode DC-DC Converters

This paper presents a new solution approach to the optimal control problem of fixed frequency switch-mode DC-DC converters using hybrid systems methodologies. In particular, the notion of the N-step model is introduced to capture the hybrid nature of these systems, and an optimal control problem is formulated and solved online, which allows one to easily incorporate in the controller design safety constraints such as current limiting. Simulation results are provided that demonstrate the prospect of this approach.

Optimal Control of the Boost dc-dc Converter

This paper extends the recently introduced approach for modelling and solving the optimal control problem of fixed frequency switch-mode dc-dc converters using hybrid system methodologies to the boost circuit topology, including parasitic elements. The concept of the ν-resolution model is employed to capture the hybrid nature of these circuits. As the resulting equations are nonlinear, two models are formulated, one featuring additional piecewise affine approximations of the nonlinearities and another nonlinear model that retains the nonlinearities in the related system description. An optimal control problem is formulated and solved online for both cases. Simulation results are provided to compare the outcomes of these approaches.

Hybrid modelling and optimal control of switch-mode dc-dc converters

This paper presents a new solution approach to the optimal control problem of fixed frequency switch-mode dc-dc converters using hybrid systems methodologies. In particular, the notion of the N-step model is introduced to capture the hybrid nature of these systems, and an optimal control problem is formulated, which allows one to easily incorporate in the controller design safety constraints such as current limiting. The optimal control problem is solved offline resulting in the explicit state-feedback controller that can be stored in a look-up table and used for the practical implementation of the control scheme. Simulation results are provided that demonstrate the prospect of this approach.